3. Start with the following statement: Vertical angles are congruent. a. State the conditional and three other forms of the statement. b. Write all 4 forms of the statement using symbols. c. If you know that a statement is true, what do you know about the truth of its converse, inverse, and contrapositive? BONUS: Use at least one truth table AND at least one property to support your reasoning.

Answers

Answer 1
Four statements driven from the original: converse: if a pair of angles are congruent, then the angles are vertical. inverse: if a pair of angles are not vertical, then the angles are not congruent. contrapositive: if a pair of angles are not congruent, then the angles are not vertical. conditional: if a pair of angles are vertical, then the angles are congruent. b) If you know that a statement is true, then its contrapositive form must be true as well.

Related Questions

There are students in three rows taking a test. there are 22 students in the first row, 19 students in the second row, and a certain number of students in the third row. if there are a total of 62 students, how many students are in the third row?

Answers

22+19+x = 62
combine like terms

41+x = 62
subtract 41 from both sides

x= 21
there are 21 students in the third row

To determine how many students are in the third row, subtract the sum of the students in the first two rows (22 + 19 = 41) from the total number of students (62). The result is that there are 21 students in the third row.

The student is asking a question related to basic arithmetic, specifically subtraction and problem-solving skills. To find out how many students are in the third row, we subtract the number of students in the first two rows from the total number of students. There are 22 students in the first row and 19 in the second row. The total number of students is 62.

So, we calculate the number in the third row as follows:

Calculate the combined number of students in the first two rows: 22 (first row) + 19 (second row) = 41 students.Subtract the number of students in the first two rows from the total number of students: 62 (total) - 41 (combined first and second rows) = 21 students.

Therefore, there are 21 students in the third row.

Kim drives 156 miles from Rotherham to London.
She drives at an average speed of 60 miles per hour.

She leaves Rotherham at 7:30 am.
Does she arrive in London before 10:00 am?

Please show all of your working out.

Answers

No. See, you can take 60 out of 156 twice and you are left with 36. This means the drive would take about 2 hours and 36 minuets. 7+2=9 30+36=66 so then you add an our the time and you get that she would arrive a few minuets afterwards. (I'm sorry if I didn't explain this very well)

Answer:

No, she will not arrive  London before 10:00 am.

Step-by-step explanation:

It is given that:

Kim drives 156 miles from Rotherham to London.

She drives at an average speed of 60 miles per hour.

i.e. in one hour she drives 60 miles.

Hence she covers 1 mile in 1/60 hours.

Now she has to travel 156 miles.

i.e. it takes her:

156/60 hours=2.6 hours.

i.e. it takes her 2 hours and 36 minutes to reach from Rotherham to London.

(

since 0.6 hours=36 minutes.

As 1 hour= 60 minutes.

so, 0.6 hours=0.6×60=36 minutes ).

Hence, if she start from Rotherham at 7:30 am.

Then she will reach London at:

7:30+2.6=10:06 am.

Hence, she will reach London after 10 am.

15+r in verbal expression

Answers

If Jimmy has to spend 15 dollars as a base value on his house, as well as a ratio, r, of his pizza earnings and time spent working everyday, he has to spend 15+r dollars on his house

How many pounds are 40kg

Answers

There are 88.1849 lb in 40 kg
Roughly 88. Each kilogram equals 2.20462 pounds.

find the inverse of f(x)=-3x+3

Answers

to get the inverse, first off do a quick switch on the variables, and then solve for "y".

[tex]\bf f(x)=y=-3x+3\qquad \qquad inverse\implies \boxed{x}=-3\boxed{y}+3 \\\\\\ x-3=-3y\implies \cfrac{x-3}{-3}=y\implies \cfrac{3-x}{3}=y\impliedby f^{-1}(x)[/tex]

Is it possible to draw a triangle with 150cm , 10cm and 10cm

Answers

No.

The two shortest legs add up to only 20 cm. This means that if attached to each end of the longest leg, they wouldn't be able to meet to form a fully closed figure.

In simpler terms, the shortest legs cannot close to form a three sided figure.

In a work-out facility, there are two racks with 40 towels per rack. on tuesday, there were 30 towels in use, on wednesday 50, and on thursday 25. what fraction, on average, is in use for the 3 days?

Answers

The capacity is 2 racks, with up to 40 towels per rack, for a maximum of 80 towels o a given day.

Tuesday: 30 towels
Wednesday: 50 towels
Thursday: 25 towels

Total towel usage for the 3 days is 30 + 50 + 25 = 105
Average usage per day is
105/3 = 35 towels per day.

Because the capacity is 80 towels, the fractional usage per day is
35/80 = 7/16

Answer:  7/16

-4(5a - 6b + 10c - 3)

Answers

The answer is:
-20a+24b-40c+12

What is the measure of ∠F?
What is the measure of ∠R?
What is the measure of ∠C?

Answers

C= 43
I'm not sure what the measure of R is, but I think the measure of F is 55°. I'm not 100% sure, which I feel terrible about, but I am positive that C= 43
:)

Answer: The measure of ∠F=55°

The measure of ∠R=36°

The measure of ∠C=43°

Step-by-step explanation:

The angle sum property of triangle say that the sum of all the interior angles of a triangle is 180 degrees.

Therefore By using angle sum property in Δ RST

∠R+∠S+∠T=180°

⇒∠R+76°+68°=180°

⇒∠R=180°-144°

⇒∠R=36°

In Δ CDE, where ∠C is a right angle.

∠C+∠D+∠E=180°

⇒∠C+90°+47°=180°

⇒∠C=180°-137°

⇒∠C=43°

In ΔDEF

∠D+∠E+∠F=180°

⇒104°+21°+∠F=180°

⇒∠F=180°-125°

⇒∠F=55°

Property of equality states that if LM = 7, and ER + LM = NP, then ___ = NP

a. LM + 7
b. ER + LM
c. ER + 7
d. 7

Answers

LM = 7.....ER + LM = NP.....ER + 7 = NP <==

Answer:

NP

Step-by-step explanation:

If a person lives to be exactly 100 years old, how many leap years will that person see

Answers

If a person lives to be exactly 100 years old, that person most likely will see 25 leap years.

given an exponential function for compounding interest, A(x)=P(1.02)^x, what is the rate of change?

Answers

[tex]\bf \qquad \textit{Amount for Exponential Growth}\\\\ A=I(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time}\\ \end{cases}\\\\ -------------------------------\\\\ \stackrel{A}{A(x)}=\stackrel{I}{P}(1.02)^{\stackrel{t}{x}}\implies A=P(1+\stackrel{r}{0.02})^x\implies \cfrac{r}{100}=0.02 \\\\\\ r=100\cdot 0.02\implies r=\stackrel{\%}{2}[/tex]

Answer:Its 2% guys

Step-by-step explanation:

Given that the legs of a right triangle measure a and b and the hypotenuse of the triangle measures c, what does the Pythagorean Theorem state about the sides of this triangle? a2 + c2 = b2 a2 − b2 = c2 2a + 2b = 2c a2 + b2 = c2

Answers

The Pythagorean Theorem is a^2+b^2 = c^2 which can be written as [tex]a^2 + b^2 = c^2[/tex]

The longest side (c) is always on its own side. This says "the squares of 'a' and 'b' add up to the square of 'c' "

The Pythagorean Theorem establishes the relationship between the sides of a right triangle, highlighting that the sum of the squares of the two shorter sides equals the square of the hypotenuse.

The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse). In mathematical terms, it is represented as a² + b² = c². This relationship applies to all right triangles and is fundamental in geometry.

One survey estimates that, on average, the retail value of a mid-sized car decreases by 8% annually. If the retail value of a car is V dollars today, which expression represents the car’s value 1 year later?

Answers

value in 1 year = V*(0.92)
V*(0.92) is the answer
hope it helps

Does prime factorization rename a composite number as the product of prime factors

Answers

Yes. Prime factorization breaks a composite number into the product of all of the prime factors which 'compose' the number.

Answer:

Yes

Step-by-step explanation:

Prime factorization does rename a composite number as the product of prime factors.

Skylar needs to buy a pair of dress pants for $40, a shirt for $30, and a tie for $20. Skylar has three coupons. The first coupon gives him x percent off on a shirt. The second coupon gives him y percent off on the dress pants. The third coupon gives him z percent off on his total purchase. He cannot combine the coupon for the total purchase with the other two coupons. These expressions give both possibilities for the total cost of Skylar's purchase after the coupons are applied. The variables represent percentages as decimals. (1−x)30+(1−y)40+20 (1−z)(40+30+20) Skylar uses the dress pants coupon. Which part of the expression represents the percent that Skylar will pay for the dress pants?

Answers

dress pants for $ 40, a shirt for $ 30, a tie for $ 20
he uses the dress pants coupon....which is the second coupon which gives him y percent off the dress pants

so ur answer is : (1 - y) * 40

Answer:

the answer is (1-y)

Step-by-step explanation:

i took the calculator and did the math and got that

What algebraic expression models the word phrase three fewer than the sum of c and d?

Answers

" the sum " means add

(c + d) - 3 <== ur expression
Sum means to add so, 
(c + d) - 3
The parenthesis are just there to keep c and d together. 

Janelle is five years younger than Louisa. In three years, Janelle will be half Louisa’s age. If j represents Janelle’s age now and l represents Louisa’s age now, which matrices represent the situation?

Answers

Answer: C

Step-by-step explanation: Got it right

Final answer:

The matrix form representing the given situation with Janelle and Louisa's ages is a system of linear equations derived from the word problem, and can be represented as: [1 -1 | -5] and [0.5 -0.5 | -1.5].

Explanation:

The question involves setting up equations based on the given word problem and representing them in matrix form. The situation describes a relationship between the ages of Janelle and Louisa, with Janelle being five years younger than Louisa. In three years, Janelle will be half of Louisa's age. This can be represented with two equations:

j = l - 5

j + 3 = 0.5 * (l + 3)

These equations can then be represented in matrix form. Matrices are used in mathematics to represent systems of linear equations, and the equations stages can be translated into a matrix where each row represents an equation:

Matrix for the system of equations:

[1 -1 | -5]

[0.5 -0.5 | -1.5]
The first row of the matrix represents the first equation, showing the coefficients of j and l, and the constant term on the right side of the equation. The second row represents the second equation with the respective coefficients and constant term.

How do you write -6.16666666... as a fraction?

Answers

       _
-6  4/9 which means it would be a repeating decimal

PLEASE HELP! GEOMETRY

Answers

The angles that occupy the same relative position at each intersection where a straight line crosses two others is called corresponding angles. If the two lines are parallel, the corresponding angles are equal.

From the prove above, it was given that line KL is parallel to line MN.
Also, angles KRQ and MSQ occupy the same relative position at the intersections R and S.

Therefore, the missing justification for the second line of the proof is "corresponding angles theorem".

At $1.25 per square foot, what is the cost of cleaning a rug with dimensions 9 feet 3 inches by 6 feet 9 inches?

Answers

 1 square foot = Cost $ 1.25 
or 
12 X 12= 144 square inches = Cost $ 1.25 

1 square inch cost = 1.25/144 = $ 0.00868 

Rug 9 feet 3 inches X 6 feet 9 inches= (9X12+3) (6X12+9) 
111 inches X 81 inches = 8991 square inches 

Total cost of cleaning the rug = 8991 X 0.00868 
= $ 78.04 

It'll cost you $ 78.04 to clean the rug

a baker starts with 4/10 kilogram. of flour to make bread he adds 3/100 kilogram of flour to his bread mixture how much total flour is used to make the bread

Answers

43/100 kilograms of flour.

Answer:

Total amount of the flour used is [tex]\frac{43}{100}[/tex] kg.

Step-by-step explanation:

Baker starts with [tex]\frac{4}{10}[/tex] kilograms of flour to make bread.

He further adds flour to his bread mixture = [tex]\frac{3}{100}[/tex] kg

Now we have to calculate the amount of flour he used to make the bread.

Total flour = [tex]\frac{4}{10}+\frac{3}{100}[/tex]

                 = [tex]\frac{40+3}{100}[/tex]

                 = [tex]\frac{43}{100}[/tex] kg

Therefore, total amount of the flour used is [tex]\frac{43}{100}[/tex] kg

A coupon subtracts $17.95 from the price P of a pair of headphones you pay $71.80 for the headphones after using the coupon write and solve an equation to find the original price of the headphones

Answers

You have to add
So the coupon subtracts 17.95 from X price and you pay $71.80 for the headphones 
17.95 + 71.80 =  $89.75 (Original Price)

Answer:

[tex]P-17.95=71.80[/tex]

Original cost: $89.75.

Step-by-step explanation:

Let P represent the original price of the headphones.

We have been given that a coupon subtracts $17.95 from the price P of a pair of headphones.

The cost of headphones after using the coupon would be [tex]P-17.95[/tex].

We are also told that you pay $71.80 for the headphones after using the coupon. We can represent this information in an equation as:

[tex]P-17.95=71.80[/tex]

Let us solve for P.

[tex]P-17.95+17.95=71.80+17.95[/tex]

[tex]P=89.75[/tex]

Therefore, the original cost of headphones is $89.75.

Solve for B.
R = x(A+B)

Answers

Work:
Solve for B
R=x (A+B)
distribute
R=Ax+Bx
-Ax both sides
R-Ax=Bx
÷x both sides
(R-Ax)/x=B
Answer: B=(R-Ax)x or B= (R/x)-A
Check your work:
Plug in B
R=x (A+(R-Ax)/x)
R=x (A+R/x-A)
R=x (R/x)
R=R

Answer is correct

1) what is the answer to 5(3x-2y)+2(x+2y)-3(3x-2y)?
a= 8x-12y
b= 8x
c= 8x-8y
d= 8xy


2) what is the answer to 2x-3+3x-5?
a= -x-8
b= 5x-8
c=-x+2
d= 5x+2

Answers

So first we want to distribute. (#1)

So, using the distributive property, we can:

5 * 3x - 2y * 5 + 2x + 2 * 2y - 3 * 3x - 3 * 2y

or

15x - 10y + 2x + 4y - 9x - 6y

Now just combine like terms

8x -12y

So for #1 it should be a.

#2: 2x - 3 + 3x - 5

Combine Like Terms: 

2x + 3x - 3 - 5

5x - 8

So it should be b.

Factor the expression y4 − 81 using the polynomial identity (x2 − y2) = (x − y)(x + y).

Answers

The factored form is (y^2+9)(y^2-9).

Plug the two terms into the equation by finding the root of both.
√y^4= y^2
√81= 9

From here, you plug the terms into the form (x+y)(x-y)
(y^2+9)(y^2-9)

Hope this helps!

What is the value of x? 3 /4 x+5− 1 /2 x=3

Answers

hello : 
(3 /4) x+5− (1 /2) x=3
(3 /4) x− (1 /2)x =3 - 5
(1/4)x = - 2
x = -8

A psychology class consists of 14 males and 36 females. if the professor selects names from the class list using random sampling, what is the probability that the first student selected will be a female? if a random sample of n = 3 students is selected and the first two are both females, what is the probability that the third student selected will be a male?

Answers

The probability of selecting a female student for the first picking is [tex] \frac{36}{50} = \frac{18}{25} [/tex]
The number of students left to select from after the first two students selected is 50 - 2 = 48 students, which consist of 34 females (two have been selected) and 14 males (none has been selected so far)
The probability that the third pick is a male is [tex] \frac{14}{48}= \frac{7}{24} [/tex]

Final answer:

The probability of selecting a female first from a class with 14 males and 36 females is 0.72. If the first two students selected are females, the probability that the third student will be a male is approximately 0.292.

Explanation:

The subject of this question is Mathematics, specifically dealing with the concept of probability in a high school level. We are to determine two probabilities: the chance of selecting a female student first from a class, and the likelihood of selecting a male student third given that the first two selected were females.

To find the probability of selecting a female first, we need to consider the total number of students and the number of females. The class has 14 males and 36 females, so the total number of students is-

14 + 36 = 50

The probability of selecting a female first is therefore the number of females divided by the total number of students, which is-

36/50 or 0.72

For the second probability, since the first two students selected are females, we now have a reduced pool of 34 females and 14 males, with a new total of 48. The probability of the third student being a male is then 14/48, which simplifies to 0.292 approximately.

A line contains the points (82, −96) and (87, −86) .

What is the slope of the line in simplified form?



Enter your answer in the box.

Answers

The slope is 2

Hopes this helps in any sort of way

Do you know the answer to this question

Answers

The correct answer is:  [C]:  "  f(x) = log₃ (x - 3) " .
_______________________________________________________
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